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3 key propositions of APT
- 1. Securities return can be described by a factor model
- 2. There are sufficient securities to diversify away idiosyncratic risk
- 3. Well functioning security market do not allow for the persistence of arbitrage opportunities
- An arbitrage opportunity exists when a zero investment opportunity produces a sure profit that will be exploited by investors regardless of their risk preference
- Arbitrage opportunities do not last long because investors will exploit it, forcing the prices to come back to normal.
Selling an asset you don't own by first borrowing the asset, then selling it (for a profit), and buying it back (at a lower price) to return it.
3 types of arbitrage opportunities
- Law of one price: 1 asset, 2 prices @ 2 places
- Perfectly correlated risks: 2 assets, 2 prices, but same risk
- Non-negative profits in all scenarios: combine assets w/ same total cost but one has higher payoff
Arbitrage Pricing Theory (APT)
- Define rP = E(RP) + βiF
- In equilibrium all well diversified PF must have the same RP relative to their beta
APT vs. CAPM
- APT based on concept that arbitrage opportunities cannot persist. It doesn't require the existence of CAPM
- CAPM applies to all securities, whereas APT leaves open the possibility that a small number of securities violate APT
- When there is a price violation in CAPM many investors will make limited PF change, while in APT few investors are needed to take large positions to restore equilibrium prices.
- ri = E(ri) + β1F1 + ... + βnFn + eiUse factor portfolios to find RPi (βi = 1 and all other β = 0)
Chen, Roll and Ross APT factors
- % chg in industrial production
- % chg in expected inflation
- % chg in unanticipated inflation
- XS return of long term bonds over government bonds
- XS return of long term government bonds over T-Bills
Fama & French (FF) model
- 1. Use diff btwn return for small & big stocks (SMB)
- 2. Use diff btwn return for stocks w/ higher ratios of book to mkt (HML)
- 2 forms of evidence that SMB & HML factors are proxies for a source of risk not captured in CAPM are (a) ability to forecast GDP growth (business cycles) and (b) time varying mkt β and mkt RP